Mean Value Theorems for Binary Egyptian Fractions

Mathematics – Number Theory

Scientific paper

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16 pages, to appear in J. Number Theory

Scientific paper

In this paper, we establish two mean value theorems for the number of
solutions of the Diophantine equation $\frac{a}{n}=\frac{1}{x}+\frac{1}{y}$, in
the case when $a$ is fixed and $n$ varies and in the case when both $a$ and $n$
vary.

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